Problem: Find the slope and y-intercept of the line that is ${\text{parallel}}$ to $\enspace {y = \dfrac{3}{2}x - 4}\enspace$ and passes through the point ${(3, 4)}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$
Solution: Parallel lines have the same slope. The slope of the blue line is ${\dfrac{3}{2}}$ , so the equation of our parallel line will be of the form $\enspace {y = \dfrac{3}{2}x + b}\enspace$ We can plug our point, $(3, 4)$ , into this equation to solve for ${b}$ , the y-intercept. $4 = {\dfrac{3}{2}}(3) + {b}$ $4 = \dfrac{9}{2} + {b}$ $4 - \dfrac{9}{2} = {b} = -\dfrac{1}{2}$ The equation of the parallel line is $\enspace {y = \dfrac{3}{2}x - \dfrac{1}{2}}\enspace$. ${m = \dfrac{3}{2}, \enspace b = -\dfrac{1}{2}}$